一种获得各向异性平面梁在任意荷载作用下弹性解的新方法

通过求解函数方程,给出了一种获得各向异性线性平面梁弹性解的新方法,该方法可以考虑任意形式的荷载以及各种端部支撑条件．将该方法与传统的逆解法或者半逆解法比较,其最大的好处在于不需要猜测应力函数的形式而直接获得问题的精确解．算例验证了该方法的正确性,同时也提供了一种求解平面梁承受任意荷载的新思路.     

一类弹性梁的能量衰减估计

研究一类弹性梁的耗散性.首先应用非线性算子半群理论证明了系统的适定性;进而运用能量方法结合乘子技巧得到弹性梁系统的能量衰减估计.     

基于曲率插值的大变形梁单元

线性梁单元的形函数在单元大转动时会引起虚假应变,不适用于几何非线性分析．传统的几何非线性梁单元由于位移插值和转角插值的相干性,常常引起剪切闭锁等问题．该文 提出了一种平面大变形梁单元,通过单元域内的曲率插值以及曲率与节点位移之间的函数关系,将单元节点力和节点位移表示为节点曲率的函数．由于曲率插值本质上是对梁的应变进行插值,保证了单元任意刚体运动不会产生虚假的节点力;且将梁的截面形心位移表示为曲率的函数,避免了传统单元中的剪切闭锁问题．因而所提方法特别适用于梁的几何非线性分析．数值算例说明了所提方法的正确性和有效性.     

Transformated Hypergraphs in Synthesis of Vibrating Beam-Systems

In this paper the characteristics of subsystems obtained by the approximate and exact method were compared, because purpose is to answer to the question ­ if the method can be used to nominate the characteristics of mechatronic systems. In this paper frequency-modal analysis have been presented for the mechanical system, that means flexibly vibrating free beam. The model of the beam was presented in the five-vertex hypergraph, which in case of approximate frequency-modal analysis we can imitate in three-vertex hypergraph. Such formulation maybe the introduction to synthesis of flexibly vibration complex beam systems with constant cross-section. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一种裂纹梁振动响应分析的近似方法

本文以线弹簧模型为基础提出了一种近似分析裂纹梁振动响应的方法.把该方法同Euler-Bernoulli梁理论、模态分析方法以及断裂力学原理等结合起来运用,导出裂纹梁振动的特征方程.作为应用实例,本文考核了简支裂纹梁和悬臂裂纹梁的固有频率响应.结果表明,本文所获得的解与现有文献中的解或实验结果取得很好的一致.     

Small scale effect on vibrational response of single-walled carbon nanotubes with different boundary conditions based on nonlocal beam models

The free vibration response of single-walled carbon nanotubes (SWCNTs) is investigated in this work using various nonlocal beam theories. To this end, the nonlocal elasticity equations of Eringen are incorporated into the various classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Reddy beam theory (RBT) to consider the size-effects on the vibration analysis of SWCNTs. The generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations of each nonlocal beam theory corresponding to four commonly used boundary conditions. Then molecular dynamics (MD) simulation is implemented to obtain fundamental frequencies of nanotubes with different chiralities and values of aspect ratio to compare them with the results obtained by the nonlocal beam models. Through the fitting of the two series of numerical results, appropriate values of nonlocal parameter are derived relevant to each type of chirality, nonlocal beam model, and boundary conditions. It is found that in contrast to the chirality, the type of nonlocal beam model and boundary conditions make difference between the calibrated values of nonlocal parameter corresponding to each one.     

Numerical Approximation and Error Analysis for the Timoshenko Beam Equations with Boundary Feedback

In this paper,the numerical approximation of a Timoshenko beam with bound- ary feedback is considered.We derived a linearized three-level difference scheme on uniform meshes by the method of reduction of order for a Timoshenko beam with boundary feedback.It is proved that the scheme is uniquely solvable,unconditionally stable and second order convergent in L_∞norm by using the discrete energy method. A numerical example is presented to verify the theoretical results.     

计算主梁绝对最大挠度的数学模型与0.618法

纵横梁桥面系统中主梁的跨度较长,纵梁上直接承受的车队荷载数量多且数值大,主梁设计中绝对最大挠度的确定是关键内容.研究了一组平行车队荷载直接沿着纵梁移动时,主梁承受结点活载下绝对最大挠度数学模型的建立;并给出了相应的计算方法,以计算机为工具,适用于任意有限多个平行移动荷载作用工况,对于主梁的设计计算与安全评估,有一定的实用价值.     

Stabilization and optimal decay rate for a non-homogeneous rotating body-beam with dynamic boundary controls

In this paper, we consider the boundary stabilization of a flexible beam attached to the center of a rigid disk. The disk rotates with a non-uniform angular velocity while the beam has non-homogeneous spatial coefficients. To stabilize the system, we propose a feedback law which consists of a control torque applied on the disk and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. By the frequency multiplier method, we show that no matter how non-homogeneous the beam is, and no matter how the angular velocity is varying but not exceeding a certain bound, the nonlinear closed loop system is always exponential stable. Furthermore, by the spectral analysis method, it is shown that the closed loop system with uniform angular velocity has a sequence of generalized eigenfunctions, which form a Riesz basis for the state space, and hence the spectrum-determined growth condition as well as the optimal decay rate are obtained.     

Recovering Beam Search: Enhancing the Beam Search Approach for Combinatorial Optimization Problems

A hybrid heuristic method for combinatorial optimization problems is proposed that combines different classical techniques such as tree search procedures, bounding schemes and local search. The proposed method enhances the classic beam search approach by applying to each partial solution corresponding to a node selected by the beam, a further test that checks whether the current partial solution is dominated by another partial solution at the same level of the search tree. If this is the case, the latter solution becomes the new current partial solution. This step allows to partially recover from previous wrong decisions of the beam search procedure and can be seen as a local search step on the partial solution. We present here the application to two well known combinatorial optimization problems: the two-machine total completion time flow shop scheduling problem and the uncapacitated p-median location problem. In both cases the method strongly improves the performances with respect to the basic beam search approach and is competitive with the state of the art heuristics.     

Analytical solution for large deflections of a cantilever beam under nonconservative load based on homotopy analysis method

In this article, large deflection and rotation of a nonlinear beam subjected to a coplanar follower static loading is studied. It is assumed that the angle of inclination of the force with respect to the deformed axis of the beam remains unchanged during deformation. The governing equation of this problem is solved analytically for the first time using a new kind of analytic technique for nonlinear problems, namely, the homotopy analysis method (HAM). The present solution can be used in wide range of load and length for beams under large deformations. The results obtained from HAM are compared with those results obtained by fourth order Range Kutta method. Finally, the load‐displacement characteristics of a uniform cantilever under a follower force normal to the deformed beam axis are presented. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27:541–553, 2011     

联合载荷作用下压杆稳定性分析

利用数学分析的基本知识建立了联合载荷作用下压杆的一般控制方程.基于两点边值问题的打靶法计算了悬臂梁在某些特定联合载荷作用下的后屈曲载荷.通过与T im oshenko用椭圆积分法所得结果进行比较,证明了方法的可行性.     

Extended multiscale FEM for design of beams and frames with complex topology

A numerical method for design of beams and frames with complex topology is proposed. The method is based on extended multi-scale finite element method where beam finite elements are used on coarse scale and continuum elements on fine scale. A procedure for calculation of multi-scale base functions, up-scaling and downscaling techniques is proposed by using a modified version of window method that is used in computational homogenization. Coarse scale finite element is embedded into a frame of a material that is representing surrounding structure in a sense of mechanical properties. Results show that this method can capture displacements, shear deformations and local stress-strain gradients with significantly reduced computational time and memory comparing to full scale continuum model. Moreover, this method includes a special hybrid finite elements for precise modelling of structural joints. Hence, the proposed method has a potential application in large scale 2D and 3D structural analysis of non-standard beams and frames where spatial interaction between structural elements is important.     

等直蜂窝夹芯盒式矩形截面梁约束弯曲应力的分析

在研究等截面蜂窝夹芯盒式矩形截面直梁自由弯曲位移和应力的基础上,分析其约束弯曲位移和应力附加项．对附加位移采用了分离变量假设,在此基础上,得到了几何、物理和平衡三方面的方程．采用伽辽金解法,使问题归结为具有衰减特性的二阶线性常微分方程．分析表明,应力衰减速度的快慢,取决于参数ν,而ν与载荷的大小、梁截面的几何尺寸以及材料的物理性质有关．     

Boundary stabilization of a Bresse‐type system

In this paper, we are concerned with asymptotic stability of a class of Bresse‐type system with three boundary dissipations. The beam has a rigid body attached to its free end. We show that exponential stabilization can be achieved by applying force and moment feedback boundary controls on the shear, longitudinal, and transverse displacement velocities at the point of contact between the mass and the beam. Our method is based on the operator semigroup technique, the multiplier technique, and the contradiction argument of the frequency domain method. Copyright © 2015 John Wiley & Sons, Ltd.     

格栅夹层梁热弯曲的等效微极热弹性分析

将格栅夹层梁热弯曲等效为微极热弹性梁的受热变形,利用平面微极热弹性理论建立了微极梁受热变形的控制方程组,给出了温度载荷下微极梁的位移表达式.通过胞元能量等效的方法,得到了研究的格栅夹层梁等效微极热弹性梁材料参数.对比了等效微极梁模型和ANSYS有限元软件计算得到的温度载荷下悬臂格栅夹层梁受热弯曲变形的数值结果,两种方法得到的结果非常接近,证明了微极热弹性梁是一种简单有效的模拟格栅夹层梁热变形的等效模型.     

A new Orthonormal Polynomial Series Expansion Method in vibration analysis of thin beams with non-uniform thickness

In this article, OPSEM (Orthonormal Polynomial Series Expansion Method) is developed as a new computational approach for the evaluation of thin beams of variable thickness transverse vibration. Capability of the OPSEM in assessing the free vibration frequencies and mode shapes of an Euler–Bernoulli beam with varying thickness is discussed. Multispan continuous beams with various classical boundary conditions are included. Contribution of BOPs (Basic Orthonormal Polynomials) in capturing the beam vibrations is also illustrated in numerical examples to give a quantitative measure of convergence rate. Furthermore, OPSEM is adopted for the forced vibration of a thin beam caused by a moving mass. Dynamics of beams supported by flexible elastic base like free to free beam on elastic foundation are also regarded. Verifications are made via eigenfunction expansion method and GMLSM (Generalized Moving Least Square Method). The very close observed agreement between the results of the two recently mentioned methods and that of OPSEM can be regarded as a guarantee of validity for the newly introduced technique. In comparison with eigenfunction expansion method, the simplicity and handiness of OPSEM in coping with different boundary conditions of the beam can be considered as its benefit for engineering practitioners.     

Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method

In this paper, a dynamic model of a complex dual rotor-bearing system of an aero-engine is established based on the finite element method with three types of beam elements (rigid disc, cylindrical beam element and conical beam element), as well as taking into account the nonlinearities of all of the supporting rolling element bearings. To rapidly and accurately analyze dynamic behaviors of the complex dual rotor-bearing system, a two-level model order reduction (MOR) method is proposed by combining component mode synthesis (CMS) method and proper orthogonal decomposition (POD) technique. The first-level reduced-order model (ROM) of the dual rotors is obtained by CMS method with a high precision for the original system. Then, the POD method is applied to second-level model order reduction to further decrease the degrees of freedom (DOFs) of first-level ROM. Second-level ROM with mode expansion and direct second-level ROM are obtained, and the nonlinear displacement responses of the two ROMs are compared with the first-level ROM. The numerical results demonstrate that the proposed method has a higher computational efficiency and accuracy in terms of mode expansion than the direct model reduction by using POD method. In addition, the nonlinear vibration responses of the dual rotor-bearing system are studied by this second-level ROM in the case of different clearances of the inter-shaft bearing. The results indicate that the dynamic characteristics of the dual rotor-bearing system are very complicated for a large clearance.     

Finite element methods for Timoshenko beam,circular arch and Reissner-Mindlin plate problems

In this paper some finite element methods for Timoshenko beam, circular arch and Reissner-Mindlin plate problems are discussed. To avoid locking phenomenon, the reduced integration technique is used and a bubble function space is added to increase the solution accuracy. The method for Timoshenko beam is aligned with the Petrov-Galerkin formulation derived in Loula et al. (1987) and can be naturally extended to solve the circular arch and the Reissner-Mindlin plate problems. Optimal order error estimates are proved, uniform with respect to the small parameters. Numerical examples for the circular arch problem shows that the proposed method compares favorably with the conventional reduced integration method.     

An optical model for implementing Parrondo’s game and designing stochastic game with long-term memory

An optical model for a photon propagating through a designed array of beam splitters is developed to give a physical implementation of Parrondo’s game and Parrondo’s history-dependent game. The winner in this optical model is a photon passed the beam splitter. The loser is a photon being reflected by the beam splitter. The optical beam splitter is the coin-tosser. We designed new games with long-term memory by using this optical diagram method. The optical output of the combined game of two losing games could be a win, or a loss, or an oscillation between win and loss. The modern technology to implement this optical model is well developed. A circularly polarized photon is a possible candidate for this physical implementation in laboratory.